-16t^2+60t+72=0

Solution for -16t^2+60t+72=0 equation:

-16t^2+60t+72=0

a = -16; b = 60; c = +72;
Δ = b2-4ac
Δ = 602-4·(-16)·72
Δ = 8208
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8208}=\sqrt{144*57}=\sqrt{144}*\sqrt{57}=12\sqrt{57}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-12\sqrt{57}}{2*-16}=\frac{-60-12\sqrt{57}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+12\sqrt{57}}{2*-16}=\frac{-60+12\sqrt{57}}{-32}
$